Problem: $g(n) = 4n^{2}-2n+h(n)$ $f(n) = 4n^{2}-5(h(n))$ $h(t) = 2t+2$ $ g(h(2)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(2)$ . Then we'll know what to plug into the outer function. $h(2) = (2)(2)+2$ $h(2) = 6$ Now we know that $h(2) = 6$ . Let's solve for $g(h(2))$ , which is $g(6)$ $g(6) = 4(6^{2})+(-2)(6)+h(6)$ To solve for the value of $g$ , we need to solve for the value of $h(6)$ $h(6) = (2)(6)+2$ $h(6) = 14$ That means $g(6) = 4(6^{2})+(-2)(6)+14$ $g(6) = 146$